Ind. Eng. Chem. Prod. Res. Dev. 1904, 23, 149-153
0.2
0.0
1 HOLD TIME
Tektronix 4662 digital plotter is used to prepare graphs. With the computer, the plots can be simple or complex. Small changes are easily shown on a new plot. The digital plotter is also used to read data from X-Y charts or strip charta. Cross hairs on the plotter arm are positioned over each data point to be read, and the plotter reads the coordinates and sends them to the computer, which stores them on disk for later analysis and plotting. This method is more accurate and faster than reading by hand.
- TENSION
u
e
: -0.2
-P
I U
149
-0.4
b
W
Conclusions Conducting elevated temperature, strain controlled creep-fatigue tests requires a number of specialized test techniques which have been described. The use of digital computers to both control tests and acquire data has proved to be extremely useful. Calculations of stress rate and strain rate are realistically possible only with computer data acquisition. Appendix Equipment Manufacturers. 1. MTS System Corporation, Minneapolis, MN 55424. 2. Lepel High Frequency Laboratories, Inc., Maspeth, New York, NY 11378. 3. Leeds & Northup, North Wales, PA 19454. 4. Three Axis Micrometer Linear Translation Stage Model 4034-M. Daedel, Inc. Harrison City, PA 15636. 5. UPS 502-1 Uninterruptable AC Power Source, Elgar Corporation, San Diego, CA 92111. 6. Digital Equipment Corporation, Maynard, MA
-0.6
-0.a
190
200 U(MPd
Figure 14. Stress rate vs. stress for tensile hold in Figure 13.
13 shows the relaxation in load which occurs during the constant strain hold period portion of the cycle. The time derivative of this curve is of interest. A point-by-point calculation of local slopes would be meaningless, but the derivative of the smoothed curve is well behaved, as shown in Figure 14. These derivatives define the stress rates during relaxation and are used to calculate strain rates. Data files generated by MTS tests are stored in binary format and must be converted to ASCII format for use with Basic programs. The files are converted with an MTS addition to Basic which reads the binary data file and makes it available to the program in ASCII one block of data a t a time. A program to convert the blocks of data to sequential files of ASCII data must be run before any data can be reduced. The result is a file of numbers between -2048 and +2047 that is normally converted to engineering units by another program. This data file is then smoothed, if necessary, and can then be fitted to a curve. The result is an analytical form which can be used in comparison with theoretical models or with data from other similar or related tests. The data can be reduced or smoothed any number of times while still preserving the original file. Even trial and error methods are much faster when using the computer and can result in better curve fits through more iterations. D. Data in Final Form. The final output of the block is the form to be used for presentation or publication. A
01754. 7. Research, Inc., Minneapolis, MN 55424. Fkgistry No. 9CrlM0,12604-41-0;steel, 12597-69-2;stainless steel, 12597-68-1.
Literature Cited Conway, J. B.; Stentz, R. H.;Berllng, J. T. “Fatlque, Tensile, and Relaxation Behavior of Stainless Steels”; Unked States Atomic Energy Commission: Oak Ridge, TN, 1975. Jones, W. B. Scr. Metall. 1982, 18, 1067-1072. Oak Ridge National Laboratory, Mechanical Properties Design Data Program Semiannual Program Report, Jan 1982. Slot, T.; Stentz. R. H.;Berllng, J. T. “Manual On Low Cycle Fatique Testing”, A w l c a n Society For Testing and Materials, STM 465, Phlladelphla, PA, 1969.
Received for review July 25, 1983 Accepted September 1, 1983
Power Rate Law Studies in Heterogeneously Catalyzed Reactions Chrlstor 0. Takoudlr School of Chembl Englneerlng, Purdue Unlverslty, West Lafayette, Indiana 47907
A new approach to the study of the kinetics and mechanisms of heterogeneously catalyzed reactlons with power rate laws is discussed and applied to carbon monoxide hydrogenation over alumina-supported ruthenium. With this method, which may suggest experiments that can discriminate among rival kinetic mechanisms and which may provide information on whether assumptions and approximations made are justified, it is shown that the existing mechanism for the reaction system mentioned above fails to predict a number of qualitative features observed. Modification(s) of this mechanism lead to no substantial improvements. Directions on future experimental studies on this reaction system are also discussed.
quires reliable kinetic models or sufficient self-consistent kinetic data available (Batchelder et al., 1982). When kinetic data are obtained they are fitted by a reaction rate expression. Then several mechanisms are tested until we
Introduction Evaluation of different reactor systems for use in indirect liquefaction via Fischer-Tropsch technology (Batchelder et al., 1982) or in other processes (Fajula et al., 1982) re0196-4321/84/1223-0149$01,50/0
0
1984 American Chemical Society
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obtain one that satisfactorily explains the experimental observations (Kellner and Bell, 1981a; Fajula et al., 1982). In many cases data are fitted in the form of a power rate law. In particular, if several reactions take place at the same time, reaction rate expressions with power rate laws seem to be favored. Such an example is the hydrogenation of carbon monoxide to olefins and paraffins (and oxygenated products) on several catalysts (Vannice, 1975,1976; Kellner and Bell, 1981a,b; Dry, 1981). The kinetics and the mechanisms of these reaction systems have been studied with an approach that involves “reasonable” approximations, assumptions, and reaction steps. This methodology leads to power rate laws that cannot predict any possible variations of an exponent of a partial pressure under varying conditions, and it can hardly provide any information that may lead to further discriminatory experiments among candidate mechanisms (Vannice, 1976; Fajula et al., 1982). Since a change in both the activation energy and the partial pressure dependence of the reaction has been observed as the Hz/CO ratio, temperature, Pco, or PH2 changes (Polizzotti and Schwarz, 1982; Fajula et al., 1982), more attention has been devoted to the explanation of these phenomena in reaction rate expressions in the form of power rate laws. Among various possibilities, one may be the existence of the superposition of a number of competing processes instead of a single rate-limiting step. Polizzotti and Schwarz (1982) have suggested that the ability of hydrogen to compete more effectively for surface sites may lead to lowering of the observed activation energy with increased H2/C0 ratio at fixed total pressure and temperature. In an earlier publication (Takoudis, 1983), a new approach to the study of the kinetics and mechanisms of heterogeneously catalyzed reactions with power rate laws has been introduced and applied to two simple reactions. That approach can suggest further experiments that can discriminate among rival mechanisms, predict changes of exponents and activation energies under varying conditions (Polizzotti and Schwarz, 1982), and provide information on whether assumptions, approximations and/or reaction steps are reasonable. The purpose of this paper is to discuss this new approach in detail and to show how one can use such a powerful analytic method in complicated reaction systems, and in particular in the carbon monoxide hydrogenation on alumina-supported ruthenium catalysts to olefins and paraffins. It is shown that the existing mechanism (Kellner and Bell, 1981b) fails to predict several qualitative features observed, even when modifications based on recent experimental findings are used (Biloen and Sachtler, 1981). In a future publication we hope to propose a comprehensive kinetics and mechanism of the FischerTropsch synthesis thoroughly examined with our approach recently introduced (Takoudis, 1983 and this study). Met hod First, some data of a reaction are fitted by a power rate law of the form r = A exp(-E/RT)fiPLXi i=l
(1)
where
Then a reaction mechanism is assumed based on experimental and any other evidence. From this mechanism, reaction rate expression(s1 may be derived as r* = r*(P,T) (2)
where P 2 PI,Pz,...,P,,. Thus, the question is whether eq 2 can be reduced to eq 1 or not, at the conditions of the experiments carried out. It is easily seen that eq 1yields a In r - xj -(3) d In Pi and (4)
Hence, we can write d In r* xj= -
(5)
a In Pj
and
because the mechanism postulated is expected to predict the kinetic data obtained. Since eq 2 does not have the form of a power rate law in general (Weller, 1956; Vannice, 1976; Carberry, 1976), eq 5 and 6 indicate that Xiand E will be functions of partial pressures of different species and of temperature. In effect, the essence of this approach is eq 3-6 and these equations may provide information which can lead to acceptance, modification, or rejection of the mechanism assumed. Carbon Monoxide Hydrogenation to Olefins and Paraffins The kinetics and mechanism of CO hydrogenation over alumina-supported Ru is now revisited and studied. Consider the reaction mechanism (Scheme I) proposed by Kellner and Bell (1981b), where equilibrium is assumed for the steps 1-3 and 5-7. Also, it is assumed that the propagation and termination steps are irreversible and that the rate coefficients for these steps are independent of the chain length, n (Storch et al., 1951; Kellner and Bell, 1981b). The equilibrium assumption for the steps 1-3 and 5-7 yields
co + s f co-s co-s + s c-s + 0-s 3 H, + 2s -+ 2H-S 4 0-S + H, -+ H,O + S n
C-S
+ H-S
5
+ H-S CH,-S + H-S CH-S
+
CH-S
-+
6 -+
-+
8
H-S
CH,-S
+ CH,-S
+S CH,-S + S CH, + 2s
CH,-S
7
CH,-S
S
-+
k to
C,H,-S
+S
C,H,-S
+ H-S
C,H,-S
+ CH,-S
--f
kP
--+
C,H,-S
C,H,
kP
--+
S
+ H-S + S
2C,H6
...
-t-
+
C,H,-S
2s
+S
Ind. Eng. Chem. Prod. Res. Dev., Vol. 23, No. 1, 1984
151
PW -.p . 2
r*c, = pk,-dc pco PH?
r*c, = pktp -OCan-l pco
and
(18)
and Since it is (Kellner and Bell, 1981a,b) OD
with p 5 K32K&.K7/K1and dc is a function of partial pressures and temperature through eq 13b. Data obtained for the first ten hydrocarbons (parafins and olefins) were fitted by power rate laws of the form (Kellner and Bell, 1981b)
we obtain
where 19, 19cnh+l. Imposing a steady-state balance on the formation of alkyl groups containing n carbon atoms, we obtain 19, =
a19n-1 = an-'191
where
I t is easy to show that
which is different from the result reported by Kellner and Bell (1981b), because one term was not accounted for in their eq 8. But note that this difference does not affect qualitatively the results of this study and of their work (Kellner and Bell, 1981a,b). Equations 8 and 11-15 yield xK1pH,8C219S
rc, = k?H2xnpcoyn
(20)
where n = 1,..., 10 for paraffins and n = 2, ...,10 for olefins. We use the notation C;, Xn-,and Yn- for paraffins and Cn=,Xn=,and Yn= for olefins. This concludes the revisiting and analysis of the mechanism and kinetics on the CO hydrogenation on alumina-supported Ru proposed by Kellner and Bell (1981b). Note that no special cases or assumptions have been made in here but the abundance of carbon monoxide adsorbed on the catalyst surface (eq 16). This mechanism is next critically studied by the methodology discussed in the previous section. Results and Discussion From eq 5 we can write for the mechanism discussed above d In r*c, x1= d In r*cl Y1 = (54 a In pHZf d In Pco
-
x,-=
+
d In r*c,
d In r*c, ; Yn- =
d In PH2
d In Pco
(5b)
and d In r*c,-
(134 where K, A, p , and Y are defined in the Nomenclature section and they are only temperature dependent. It is assumed that the fraction of vacant surface sites can be expressed as 1
where K1 is the equilibrium constant for reaction step 1 (Kellner and Bell, 1981b). Recent experimental evidence seems to support the validity of eq 16 (Cant and Bell, 1982). Thus, eq 13a becomes
(13b) Because 1 9 ~cannot be an explicit function of partial pressures and temperature (eq 13b), Kellner and Bell (1981b) considered two cases: first X = 0 and a = constant, and second p = 0. In using the method we discussed previously, we do not have to consider any special cases and therefore we will not. Based on the above, the production rates of hydrocarbons are
xn== a In PH2' *
d In r*cn-
yn==
d In Pco
(54
Equations 5a, 13b, and 17 yield X 1 < 1.5 and Yl < -1 for any possible values of the physical parameters involved. These results are consistent with the rate expression reported by Kellner and Bell (1981b) (within experimental error), but they disagree with exponents reported by other investigators (Vannice, 1975; Dalla Betta et al., 1974). Equations 5b, 13b, and 18 yield X ; > Xn-l-and Y; > Y n - iunder any conditions -for the mechanism described previously. A look at Table I reported by Kellner and Bell (1981b) indicates that they observed in general Y; > Yn-l-, in agreement with the prediction just mentioned, and X; C X,i which is opposite to the prediction discussed above. Although some irregularities were observed in the trends of the magnitudes of X; and Y; (Kellner and Bell, 1981b) as n increased, it is clear from the above analysis that X,is predicted to change in the opposite direction from that observed, and that no such irregularities are predicted. For olefins, Table I of that same reference (Kellner and Bell, 1981b) indicates that the magnitude of Xn=decreases and of Yn=increases substantially as the carbon number n increases from 2 to 10. Our analysis on eq 5c, 13b, and 19 yields Xn=> Xn-l=,which is opposite to the observations mentioned above, and Y,' > Yn-l=, in agreement with experimental results. Note that the results-predictions
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Ind. Eng. Chem. Prod. Res. Dev., Vol. 23, No. 1, 1984
discussed here are valid for any values of the physical parameters involved. Application of our methodology to a,the probability of chain propagation, yields aa/dPt > 0. This suggests that under constant PH,/PcO ratio and temperature a increases as the total pressure increases. In particular, it is seen that a increases substantially when Pt increases. This result agrees with the predictions reported by Kellner and Bell (1981b) and it disagrees with their experimental findings reported in Table V of that publication. Furthermore, with the method discussed above it can be shown that aa/dPH2 > 0 and da/dPco > 0. These suggest that under constant Pco and temperature or constant PH, and temperature, the probability of chain propagation should increase when PH, or Pco increases, respectively. Summarizing our results so far, we see that the existing mechanism on carbon monoxide hydrogenation over alumina-supported ruthenium (Kellner and Bell, 1981b) fails to predict many qualitative features observed. Also, to emphasize the merit of the methodology introduced recently, we point out that the inadequacy of the mechanism discussed previously has been established with no quantification of any physical parameters. Our only assumptions have been the mechanism introduced by Kellner and Bell (1981b),the abundance of CO on the catalyst surface, and that the Langmuir adsorption postulates are quantitatively valid. In fact, the last of these assumptions can be relaxed with no overall significant changes in the analysis presented above (Weller, 1956; Carberry, 1976). Once the inadequacies of this mechanism (reaction steps 1-12) are realized, the next thought is modification(s) of the reaction mechanism discussed above or reconsideration of the assumption that carbon monoxide is the abundant adsorbed species on Ru. Two modifications were attempted. First, reaction step 4 was broken into two steps
+ H-s 5 OH-s + s OH-S + H-S 5 H 2 0 + 2s
(4a) 0-s (4b)
This led to no qualitative change of the results discussed previously. However, a was a weaker function of total pressure than it was previously, X1and Yl had to assume smaller values than the ones in the mechanism discussed above, and the inequalities X,-> X,-l- and X,=> X,-l= were weaker than before. A second modification was the assumption of different termination steps, mainly for the olefin formation. One such termination step was (loa) C2H5-S + CH2-S C,H4 + CH3-S + S
-
Our motivation for such a change was twofold: first, the probability of chain length is not strongly dependent on reactor pressure Pt (Kellner and Bell, 1981b);and second, it appears that the magnitudes of X, and Y,, follow the trends X,, < X,-l and Y,, > Y,,-l,for any carbon number n. Thus,if reaction step 10a instead of step 10 is accounted for, then both objectives just mentioned are achieved. But this "new" mechanism does much worse in other respects. For example the ratio r*c,-lr*c - now becomes proportional to a positive power of the t o d pressure, in contradiction to experimental observations (Figure 9 of Kellner and Bell, 1981b). Therefore, either modification or both yield no overall improvement of the reaction mechanism discussed above. Recent experimental evidence indicates that CO and carbon are the abundant surface species on catalysts for similar carbon monoxide hydrogenation systems (Biloen and Sachtler, 1981). This modifies the assumption that
CO-S is the dominant adsorbed species. Based on that recent evidence it is 19~0 t9c = 1, and the application of our methodology yields no overall improvement of the mechanism discussed previously. However, note that the analysis of this system now becomes tedious, although all qualitative features can be done and checked analytically. This concludes our attempts to possibly improve or justify the reaction mechanism for the carbon monoxide hydrogenation on alumina-supported ruthenium catalysts proposed by Kellner and Bell (1981b). Many inadequacies of this mechanism have already been clear. Recent experimental studies have pointed out that two types of surface carbon and of adsorbed CO on the catalyst surface exist (Biloen and Sachtler, 1981). Perhaps, such considerations should be taken seriously in any future attempts to model carbon monoxide hydrogenation on various catalysts. Although Biloen and Sachtler (1981) and Brady and Pettit (1980, 1981) seem to present evidence supporting the initiation and propagation steps considered in the mechanism discussed above, further studies are required for these steps as well as for the termination steps. However, perhaps the most intriguing result in here is that we now have the analytic tools to test mechanisms and kinetics so that they may eventually predict all experimental observations.
+
Conclusion A new approach to studying the kinetics and mechanisms of heterogeneously catalyzed reactions, whose rate expressions were in the form of a power rate law, was discussed. This approach may check whether assumptions or approximations made are justified and it may suggest further discriminatory experiments among rival mechanisms. A thorough analysis of the existing reaction mechanism of CO hydrogenation on alumina-supported Ru catalysts indicates that many qualitative features observed cannot be predicted by this mechanism or a number of modified versions of it. A preliminary agreement between reaction kinetics and a proposed mechanism may be misleading and may result in a premature acceptance of a mechanism. Hence, a justification of assumptions made and discriminatory experiments among rival reaction mechanisms are required. The analytic tools for such studies are available and powerful even in very complicated reaction systems such as the Fischer-Tropsch synthesis. Nomenclature A = preexponential factor E = activation energy H2/C0 = molar ratio of hydrogen over carbon monoxide I-S = adsorbed species I on the catalyst surface k = rate constant K = equilibrium constant Pi = partial pressure of the species i Pt = total pressure r = reaction rate determined from data r* = reaction rate determined from an assumed mechanism rc, = production rate of a hydrocarbon with n carbon atoms per molecule R = universal gas constant S = vacant surface site of the catalyst surface T = temperature Xn-(Xn=)= exponential of the partial pressure of H2in a power rate law for the formation of a paraffin (olefin) with n carbon atoms per molecule X i= exponent of the partial pressure of species i (eq 1) Y J Yn=)= exponent of the partial prexxure of CO in a power rate law for the formation of a paraffin (olefin) with n carbon atoms per molecule
Ind. Eng. Chem. Prod. Res. Dev. 1984, 23, 153-162 CY
= probability of chain propagation
density) of species i
Registry No. Carbon monoxide, 630-08-0;ruthenium, 144018-8. Literature Cited Batchelder. R. F.; Pennllne, H. W.; Schehl, R. R. Technlcal Publication DOE/ PETC/lR-83/6, US. Dept. of Energy, Pittsburgh, PA, Aprll 1982. B l h n , P.; Sachtler, W. M. H. A&. Catal. 1981, 30. 165-216. Brady, R. C.. 111; Pettit, R. J . Am. Chem. Soc. 1980, 102, 6181-2. Brady. R. C., 111; Pettit, R. J . Am. Chem. Soc. 1981, 103. 1287-9. Cant, N. W.; Bell, A. T. J . Catel. 1982, 73, 257-271. Carbemy, J. J. “Chemlcal and Catalytic Reaction Engineering”; McGraw-HIII: New Ywk, 1976.
153
Daih Betta, R. A.; Plken, A. G.; Shelef, M. J . Catal. 1974, 35, 54-60. Dry, M. E. “Catalysis. Sclence and Technology”; Sprlnger-Verlag: Berlin, West Qermeny. 1981. Fajula, F.; Anthony, R. G.; Lunsford, J. H. J . Catel. 1982. 73, 237-256. Kellner, C. S.; Bell, A. T. J . Catel. 1981a, 71. 296-307. Keilner, C. S.; Bell, A. T. J . Catel. 198lb, 70. 418-432. PoIIzzottl, R. S.; Schwerz, J. A. J . Catel. 1982, 77, 1-15. Storch, H. H.; Golumblc. N.; Anderson, R. B. “The Flscher-Tropsch and Related Syntheses”; Wlley: New York, 1951. Takoudls, C. G. J . Catal. 1989, 79, 281-5. Vannlce, M. A. J . Catel. 1975, 37, 462-473. Vannlce, M. A. Catal. Rev. Sci. Eng. 1978. 14, 153-191. Weller, S. A I M J . 1956, 2 , 59-62.
Received for review August 22, 1983 Accepted September 26, 1983 This work was partially supported by CONOCO, Inc., and NALCO Chemical Company through grata to the Purdue Coal Research
Center.
Preparation and Characterization of Composite Hollow Fiber Reverse Osmosis Membranes by Plasma Polymerization. 1 Design of Plasma Reactor and Operational Parameters P. J. Heffernan, K. Yanaglhara, Y. Matruzawa, E. E. Hennecke, E. W. Hellmuth, and H. Yasuda” Department of Chemical Engineering and Graduate Center for Materiels Research, Unhwsity of Mlssouri-Rolie, Rolle, Mlssouri 65401
Composite hollow fiber reverse osmosis membranes were prepared by depositing a thin layer (10-50 nm) of plasma polymers on hollow fibers wlth porous walls (made of polysulfone). The coating was canied out in a semicontinuous manner with six strands of substrate fibers. Operational parameters which influence reverse osmosis characteristics of composRe membranes were investigated.
Introduction Thin film formation which occurs in glow discharge of organic vapors is generally referred to as “glow discharge polymerization” or “plasma polymerization”. Polymers formed by plasma polymerization of a monomer (e.g., styrene) are considerably different from the polymer formed from the same monomer by conventional polymerization processes. Furthermore, many organic compounds which are not considered as monomers for polymerization can be polymerized by plasma polymerization. In many cases, plasma polymers (polymers formed by plasma polymerization) are prepared in networks of highly branched and highly cross-linked segments. Polymers deposit onto a substrate material placed in glow discharge from low-pressure plasma (partially ionized state of vapor). Because of interaction of plasma with the substrate polymer and of the unique mechanisms of polymer formation, excellent adhesion of a thin deposit to the substrate can be obtained. Typical plasma polymers are commonly amorphous and thin films without macroscopic pinholes can be readily obtained. Because of these advantageous features of plasma polymerization, an ideal composite reverse osmosis membrane can be prepared by plasma polymerization if the right selection of porous substrate and the proper execution of plasma polymerization are combined. The potential uae of plasma polymerization for membrane preparation has been demonstrated in several papers published in recent years (Buck and Davar, 1970; Hollahan and Wy0196-4321/84/1223-0153$01.50/0
deven, 1973; Yasuda et al., 1973(a), 1975,1976; Bell et al., 1975), and some noteworthy unique characteristics of plasma polymerized membranes have also been reported (Yasuda and Lamaze, 1973a): for example, (1)very stable performance independent of salt concentration and applied pressure; (2) salt rejection and water flux both increase with time in the initial stage of reverse osmosis resulting in improvement of reverse osmosis membrane performances with the time of operation; (3) high salt rejection (over 99%) with high water flux (up to 38 gfd) obtained with 3.5% NaCl salt solution; and (4) the prepared membranes were chemically durable. On the other hand, however, all membranes by plasma polymerization are prepared in relatively small laboratory scale batch processes, and data available are insufficient to judge the true practicability of the method in large-scale applications. Many practitioners of membrane technology, with lack of fundamental knowledge about the method, have failed to recognize the potential of plasma polymerization in membrane preparation. The most frequently raised questions, or expressions of doubt about the practicability of the method, are concerned with (1) reproducibility of the process and (2) difficulty of scale-up for a continuous operation. Therefore, the major objectives of this study are focused on these two factors. In order to investigate the reproducibility and the feasibility of continuous operation, semicontinuous plasma polymerization utilizing hollow fibers as substrates was chosen and a special tandem reactor was constructed. 0 1984 American Chemical Society
